Emperor Alexis was the first (out of four) members of the Komennos Dynasty, who instituted the Komnenos reforms.
Because it was (initially) a "faction" of the Byzantine Empire, rather than representatives of the Empire itself, they went back to using their own "native" troops of peasant soldiers, rather than mercenaries. The defeat at Manzikert had made this possible by decimating the former Byzantine military class (which favored using mercenaries), plus the loss of the mercanaries themselves.
Using troops from their original bases in the Balkans, first Alexius then his son John had to first defeat European invaders of the Balkans, such as the Pechenengs and the Hungarians. These successes built up the strength of the Komnenon army, which was then able to wrest much of the Black Sea coast and the western coast of modern "Turkey" from the Seljuks.
It was a see-saw fight for about a century, but the Komnenos were much better defenders of the Byzantine empire than their predecessors. When they finally lost a battle against the Turks at Mynkephalon, in 1176, it was a far less decisive defeat than that at Manzikert a century earlier.